A uniform rod of mass m and length l is at rest on smooth horizontal surface. An impulse P is applied to end B as shown.

Distance travelled by the centre of the rod, while rod rotates by `90^(@)`

Options

A. `(pi l)/(7)`
B. `(pi l)/(4)`
C. `(pi l)/(12)`
D. `(pi l)/(5)`

Answer

C

Explanation

angle rotated `= (pi)/(2)` and we know that `theta = omega t`
`rArr t = (theta)/(omega) rArr t = ((pi)/(2))/((6P)/(mL)) rArr t = (pi mL)/(12P)`
Distance covered by centre of rod.
`s = v xx t rArr s = (P)/(m) xx (pimL)/(12P) rArr s = (pi L)/(12)`